This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A337719 #33 Sep 26 2020 11:41:01 %S A337719 1,2,4,8,16,32,44,72,128,220,380,620,1232,2400,3988,7008,14260,25512, %T A337719 50944,105560,197880,381432,785984,1443992,2981200,6623144,13044340, %U A337719 26020924,55781760,108592260,231819360,526660160,1071224176,2231977656,4950184948,10009562624 %N A337719 The number of maximally large absolute-difference triangles consisting of positive integers <= n. %C A337719 a(17) is the first term that is more than twice its predecessor. %C A337719 All terms after a(2) are divisible by four. This is because valid starting layers (of length greater than two) produce distinct valid starting layers when subjected to either or both of two transformations. %C A337719 . %C A337719 1 1 %C A337719 2 1 1 2 %C A337719 1 3 2 2 3 1 %C A337719 * | * %C A337719 * | * %C A337719 * | * %C A337719 ------|------ %C A337719 * | * %C A337719 * | * %C A337719 * | * %C A337719 3 1 2 2 1 3 %C A337719 2 1 1 2 %C A337719 1 1 %C A337719 . %C A337719 There is the obvious reflection about the y-axis (reversal), and there is the somewhat less obvious reflection about the x-axis. Reflection about the x-axis is valid because absolute differences are maintained. Note that it is not possible for a solution to be equivalent to any of its own transformations. If it were, the base layer or the layer that succeeds it would need to be palindromic. This is invalid because any absolute-difference triangle with a palindromic base and a height greater than one is topped with a zero. %H A337719 Samuel B. Reid, <a href="/A337719/a337719_1.py.txt">Python program for A337719</a> %H A337719 Samuel B. Reid, <a href="/A337719/a337719_1.c.txt">C program for A337719</a> %e A337719 a(5) = 16 %e A337719 . %e A337719 1 2 5 1 2 3 2 5 1 2 3 4 1 5 4 5 4 1 5 4 %e A337719 1 3 4 1 1 3 4 1 1 3 4 1 1 3 4 1 %e A337719 2 1 3 2 1 3 2 1 3 2 1 3 %e A337719 1 2 1 2 1 2 1 2 %e A337719 1 1 1 1 %e A337719 . %e A337719 3 1 5 4 2 3 5 1 2 4 1 4 5 1 4 5 2 1 5 2 %e A337719 2 4 1 2 2 4 1 2 3 1 4 3 3 1 4 3 %e A337719 2 3 1 2 3 1 2 3 1 2 3 1 %e A337719 1 2 1 2 1 2 1 2 %e A337719 1 1 1 1 %e A337719 . %e A337719 2 4 5 1 3 4 2 1 5 3 2 5 1 2 5 4 1 5 4 1 %e A337719 2 1 4 2 2 1 4 2 3 4 1 3 3 4 1 3 %e A337719 1 3 2 1 3 2 1 3 2 1 3 2 %e A337719 2 1 2 1 2 1 2 1 %e A337719 1 1 1 1 %e A337719 . %e A337719 2 1 5 2 1 2 1 5 2 3 4 5 1 4 3 4 5 1 4 5 %e A337719 1 4 3 1 1 4 3 1 1 4 3 1 1 4 3 1 %e A337719 3 1 2 3 1 2 3 1 2 3 1 2 %e A337719 2 1 2 1 2 1 2 1 %e A337719 1 1 1 1 %e A337719 . %o A337719 (Python and C) See Links section. %Y A337719 Cf. A062684, A094225. %K A337719 nonn %O A337719 1,2 %A A337719 _Samuel B. Reid_, Sep 16 2020